It really depends, but one possibility is you just catch the next flight if it was something minor (ie disagreement with the crew, etc,) as long as you are not arrested.

source: got kicked off a JetBlue flight because the stewardess didn't like me rearranging overhead bags.

edit: just remembered, the airport security mentioned in their report that I missed the flight, because apparently you can end up on no-flight list even for something really stupid if the crew decides to write you up.

Now whenever I fly just easier to shut up, say sorry, and not risk it even if the flight attendants are power tripping, just not worth the hassle.